Bulletin of Mathematical Biology最新文献

Mammalian cells regulate their glucose levels by redistributing glucose transporter proteins within the cell. Glucose Transporter 4 (GLUT4) is the main insulin-regulated glucose transporter in mammalian cells. Insulin signals the redistribution of GLUT4 from intracellular compartments to the cell surface. The mechanisms of the release of GLUT4 and subsequent transport to the plasma membrane remain an open question. Here, a biologically plausible model of GLUT4 translocation is presented. Using a stochastic queuing model, we find that changing only the number of fusion sites available for GLUT4-containing vesicles as a function of insulin is sufficient to explain experimental observations. Thus, the activity of the fusion sites could be the primary determinant of the dynamics of GLUT4.

Mycoplasma pneumoniae (Mp) is one of the most common causes of community-acquired pneumonia in children. To uncover the effective interventions during an epidemic in crowded settings, we first develop a novel staged progression ordinary differential equation model for the transmission of Mp, incorporating the effects of isolation measures and correct diagnosis rate. The basic reproduction number is obtained by the next generation matrix approach. Based on the deterministic model, a continuous-time Markov chain (CTMC) model is formulated to account for demographic variability. An analytic estimate for the probability of a disease outbreak, as well as an explicit expression for the mean (variance) of the disease extinction time in the absence of an outbreak, is derived by a multi-type branching process approximation of the CTMC model. By fitting the model to real data from a primary school, we estimate some key parameters of our model. Numerical simulations indicate that: (i) if the effects of demographic variability are ignored, the time to extinction after an outbreak is likely to be significantly underestimated or overestimated, depending on the isolation proportion; (ii) the impact of disease transmission rate, isolation proportion, and correct diagnosis rate on the probability of a disease outbreak depends on the stage of infection in which an infected individual is first introduced; (iii) decreasing the transmission rate, increasing the isolation proportion, or improving the correct diagnosis rate can significantly reduce the mean final size after an outbreak; and (iv) improving the correct diagnosis rate can help reduce the number of severe pneumonia cases.

In this work we present a C-MATH-NN framework that extends a C-MATH framework that was developed in recent years to include prediction using artificial neural networks (NN) in a way that is engaging, interdisciplinary and collaborative to help equip our next generation of students with advanced technological and critical thinking skills motivated by social good. Specifically, the C-MATH framework has successfully helped students understand a real-world Context through a mathematical Model which is then Analyzed mathematically and Tested through appropriate numerical methods with data, and finally this undergraduate research becomes a Habit for students. Furthermore, the explanation of the main components of a simple NN-model serves as an introduction to this popular artificial intelligence tool. This framework has contributed to the success of talented students in mathematical biology research and their academic goals. We present a visual introduction to the architecture of artificial neural networks and its application to disease dynamics for all interested learners. We introduce a simple feed forward physics-informed neural network (PINN) built in MS-Excel that works very well for an epidemiological model and an equivalent Python implementation that is robust and scalable. The products introduced in this work are shared in an online repository with curriculum material for students and instructors that includes MS-Excel workbooks and Python files to facilitate the acquisition of technology tools to explore and use in their own projects.

The community composition of vectors and hosts plays a critical role in determining risk of vector-borne disease transmission. Aedes aegypti and Aedes albopictus, two mosquito species that both transmit the viruses that cause dengue, chikungunya, and Zika, share habitat requirements and compete for resources at the larval stage. Ae. albopictus is generally considered a better competitor under many conditions, while Ae. aegypti is able to tolerate higher temperatures and is generally a more competent vector for many pathogens. We develop a stage-structured ordinary differential equation model that incorporates competition between the juvenile stages of two mosquito populations. We incorporate experimental constraints on competition coefficients for high and low quality food resources and explore differences in the potential outcomes of competition. We then incorporate temperature-dependent fecundity rates, juvenile development rates, and adult mortality rates for each species, and we explore competition outcomes as a function of temperature. We show that regions of coexistence and competitive exclusion depend on food quality and relative values of temperature-dependent life history parameters. Finally, we investigate the combined impacts of temperature and competition on the potential for dengue transmission, and we discuss our results in the context of present and future risk of mosquito-borne disease transmission.

A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are accommodated. A sufficient condition for the local asymptotic stability of a coexistence equilibrium in this system is then proven. Using this system, the generalisation of the Beverton-Holt and Leslie-Gower models of competition to multispecies systems with possible maturation delays is presented and shown to yield interesting stability properties. The stability of coexistence depends on the relative abundances of the species at the unique interior equilibrium. A sufficient condition for local stability is derived that only requires intraspecific competition to outweigh interspecific competition. The condition does not depend on maturation delays. The derived stability properties are used to develop a novel estimation approach for the coefficients of interspecific competition. This approach finds an optimal configuration given two conjectures. First, coexisting species strive to outcompete competitors. Second, persisting species are more likely in stable systems with strong dampening of perturbations and high ecological resilience. The optimal solution is compared to estimates of niche overlap using an empirical example of malaria mosquito vectors with delayed maturity in the Anopheles gambiae sensu lato species complex.

Phylogenetic networks are graphs that are used to represent evolutionary relationships between different taxa. They generalize phylogenetic trees since for example, unlike trees, they permit lineages to combine. Recently, there has been rising interest in semi-directed phylogenetic networks, which are mixed graphs in which certain lineage combination events are represented by directed edges coming together, whereas the remaining edges are left undirected. One reason to consider such networks is that it can be difficult to root a network using real data. In this paper, we consider the problem of when a semi-directed phylogenetic network is defined or encoded by the smaller networks that it induces on the 4-leaf subsets of its leaf set. These smaller networks are called quarnets. We prove that semi-directed binary level-2 phylogenetic networks are encoded by their quarnets, but that this is not the case for level-3. In addition, we prove that the so-called blob tree of a semi-directed binary network, a tree that gives the coarse-grained structure of the network, is always encoded by the quarnets of the network. These results are relevant for proving the statistical consistency of programs that are currently being developed for reconstructing phylogenetic networks from practical data, such as the recently developed SQUIRREL software tool.

Ligand-receptor interactions are fundamental to many biological processes. For example in antibody-based immunotherapies, the dynamics of an antibody binding with its target antigen directly influence the potency and efficacy of monoclonal antibody (mAb) therapies. In this paper, we present an asymptotic analysis of an ordinary differential equation (ODE) model of bivalent antibody-antigen binding in the context of mAb cancer therapies, highlighting the complexity associated with bivalency of the antibody. To understand what drives the complex temporal dynamics of bivalent antibody-antigen binding, we construct approximate solutions to the model equations at different timescales that are in good agreement with numerical simulations of the full model. We focus on two scenarios: one for which unbound antigens are abundant, and one for which they are scarce. We show how the dominant balance within the model equations changes between the two scenarios. Of particular importance to the potency and efficacy of mAb treatments are quantities such as antigen occupancy and bound antibody number. We use the results of our asymptotic analysis to estimate the long-time values of these quantities that could be combined with experimental data to facilitate parameter estimation.

This work presents a three-dimensional fully-coupled fluid-structure interaction (FSI) model of a pulsing soft coral polyp where the movement of the tentacles is driven by a prescribed active tension during contraction with a passive expansion due to the elastic behavior of the tentacles. The resulting motion of the tentacles is emergent rather than prescribed. This approach allows one to determine how the coral's underlying morphology, mechanics, and neural activation affect its kinematics and the resulting fluid motion, which has implications for soft robotic design. More specifically, one can easily vary the maximum tension exerted by the coral, the elasticity of the model coral body, and the pulsation frequency to understand how altering neuromechanical parameters affects the flux above the coral and the energy required to pulse actively. When the parameters are tuned such that the emergent motion is similar to that measured for live coral, a large amount of upward flux is generated for a relatively low energy expenditure. Additionally, a circulation analysis reveals the generation of stopping and starting vortices with each pulse cycle, as seen in other Cnidarians such as jellyfish. We find that the relationship between kinematics, upward flux, circulation, and the polyp's active and passive material properties is highly complex. Our results suggest that the corals operate at or near an energetically favorable regime. This work further increases our understanding of how and when sessile organisms should expend energy to actively pulse to enhance nutrient exchange.

Measures of tree balance play an important role in many different research areas such as mathematical phylogenetics or theoretical computer science. Typically, tree balance is quantified by a single number which is assigned to the tree by a balance or imbalance index, of which several exist in the literature. Most of these indices are based on structural aspects of tree shape, such as clade sizes or leaf depths. For instance, indices like the Sackin index, total cophenetic index, and $\hat{s}$ -shape statistic all quantify tree balance through clade sizes, albeit with different definitions and properties. In this paper, we formalize the idea that many tree (im)balance indices are functions of similar underlying tree shape characteristics by introducing metaconcepts of tree balance. A metaconcept is a function ${\Phi }_f$ that depends on a function f capturing some aspect of tree shape, such as balance values, clade sizes, or leaf depths. These metaconcepts encompass existing indices but also provide new means of measuring tree balance. The versatility and generality of metaconcepts allow for the systematic study of entire families of (im)balance indices, providing deeper insights that extend beyond index-by-index analysis.